LNSS Onboard Ephemeris-Aided Kalman Filter for Clock Synchronization in Low Visibility Conditions

Accurate synchronization to GPS Time (GPST) is a fundamental requirement for the emerging Lunar Navigation Satellite System (LNSS). Given the stringent size, weight, and power constraints of CubeSat-based architectures, these platforms typically employ miniature oscillators such as Chip Scale Atomic Clocks (CSACs). Unlike high-stability ground references, these onboard clocks exhibit significant drift and require frequent corrections. However, LNSS satellites in Elliptical Lunar Frozen Orbits (ELFOs) frequently encounter signal-deprived environments where fewer than four GPS satellites are visible. In such underdetermined scenarios, standard positioning algorithms fail to resolve the navigation solution and revert to a prediction-only coasting mode, resulting in unbounded clock error growth. Unlike previous lunar GNSS approaches that primarily exploit sparse measurements to sustain navigation solutions, this work instead focuses on directly constraining onboard clock errors under limited visibility. To overcome this limitation, this paper proposes a novel LNSS onboard ephemeris-aided Kalman filter (EA-KF). Instead of discarding sparse measurements, the proposed architecture explicitly incorporates onboard ephemeris information to fuse the available one to three pseudorange observations, treating the satellite trajectory as a stochastic geometric constraint. The performance of the EA-KF was evaluated using a high-fidelity simulation framework. To ensure realistic geometry, the GPS and ELFO trajectories were modeled using IGS precise ephemeris and JPL Horizons lunar motion data. Realistic clock behavior was derived from CSAC hardware measurements, with atmospheric delays removed to emulate the lunar vacuum. Furthermore, SNR-dependent noise reflecting the increased free-space path loss in lunar orbit was incorporated into the pseudorange observations. Results demonstrate that the proposed method significantly outperforms conventional coasting techniques specifically during sparse-visibility intervals. In low-visibility conditions (1 ? N ? 3), the EA-KF reduced the root mean squared error (RMSE) of clock synchronization by 59.34% and 88.21% across two representative lunar orbital scenarios. These findings indicate that leveraging onboard orbital information as a geometric constraint is an effective strategy for maintaining precise timing in low-cost lunar navigation constellations.